The Brainiac Family Tree

According to what I've read Brainiac 1 (Superman's longtime nemesis) is father to Brainiac 2, who in turn is father to Brainiac 3...But from then on I'm unsure as to how the family tree progresses. Brainiac 5 of the Legion of Super Heroes is supposed to be the child of Brainiac 4, but I'm a bit confused because according to comicvine the name Brainiac 4 refers to both his mother AND his father, and since Brainiac 5 is from the future I'm unsure how distantly related Brainiac 4 is to Brainiacs 2 & 3.

Oh, and apparently Brainiac 8/Indigo comes from even further in the future than Brainiac 5, and there had to have been a Brainiac 6-7 as well at somepoint (so no idea how they're connected to the rest of the Brainy family tree).

There is indeed Brainiac, Vril Dox Jr (that is what he is almost always known for, but he is also called Brainiac 2 only briefly), Lyrl Dox, who demands to be called Brainiac 3, and then there's Brainiac 5 in the future, and there are mentions of a Brainiac 6, who programmed Indigo, and there is also a Brainiac 13 from the 64th century.

The thing is, though, Brainiac 5, and presumably all of the following Brainiacs, do not come from Lyrl Dox/Brainiac 3. In the first volume of the most recent R.E.B.E.L.S. series, a hologram of Brainiac 5 tells Vril that if he dies, the Dox line dies with him. This is after the birth of Lyrl, so it maybe means that Lyrl will die soon, or he is just not the ancestor to all the other Brainiacs, and Dox will have another child.

After Brainiac 3, the Brainiac name is forgotten for a thousand years until B5's father reclaims it in an attempt to clear his family's name, becoming Brainiac 4. He gives his son the same purpose, and he takes the name Brainiac 5.

Pre Crisis there were only 5 Brainiacs. as stated in Secrets of the Legion of Super-heroes. Brainiac adopted Vril Dox, had a son called Pran Dox who had a son called Kajz Dox who was the father of Querl Dox. This presumes Coluans lived a very long time.